Construction of Entire Modular Forms of Weights 5 and 6 for the Congruence Group Γ0(4N)

1995 ◽  
Vol 2 (2) ◽  
pp. 189-199
Author(s):  
G. Lomadze
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Congruence Subgroup ◽  
Congruence Group

Abstract Two classes of entire modular forms of weight 5 and two of weight 6 are constructed for the congruence subgroup Γ0(4N). The constructed modular forms as well as the modular forms from [Lomadze, Georgian Math. J. 1: 53-76, 1994] will be helpful in the theory of representation of numbers by the quadratic forms in 10 and 12 variables.

On Some Entire Modular Forms of Weights 5 and 6 for the Congruence Group Γ0(4N)

1994 ◽  
Vol 1 (1) ◽  
pp. 53-76
Author(s):  
G. Lomadze
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Congruence Subgroup ◽  
Congruence Group ◽  
Positive Integers

Abstract Two entire modular forms of weight 5 and two of weight 6 for the congruence subgroup Γ0(4N) are constructed, which will be useful for revealing the arithmetical sense of additional terms in formulas for the number of representations of positive integers by quadratic forms in 10 and 12 variables.

On Some Entire Modular Forms of Weights and for the Congruence Group Γ0(4N)

1996 ◽  
Vol 3 (5) ◽  
pp. 485-500
Author(s):  
G. Lomadze
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Congruence Group ◽  
Positive Integers

Abstract Entire modular forms of weights and for the congruence group Γ0(4N) are constructed, which will be useful for revealing the arithmetical sense of additional terms in formulas for the number of representations of positive integers by quadratic forms in 7 and 9 variables.

On Entire Modular Forms of Half-Integral Weight on the Congruence Subgroup Γ0(4N)

2004 ◽  
Vol 11 (1) ◽  
pp. 111-123
Author(s):  
G. Lomadze
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Congruence Subgroup ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Positive Integers

Abstract Some entire modular forms of weight on the congruence subgroup Γ0(4N) are constructed if s is odd > 11. The constructed type of entire modular forms is useful for revealing the arithmetical meaning of additional terms in formulas for the number of representations of positive integers by positive quadratic forms with integral coefficients if the number s of variables is odd > 11.

On Some Entire Modular Forms of an Integral Weight for the Congruence Subgroup Γ0(4𝑁)

1999 ◽  
Vol 6 (5) ◽  
pp. 471-488
Author(s):  
G. Lomadze
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Congruence Subgroup ◽  
Integral Weight ◽  
Positive Integers

Abstract Four types of entire modular forms of weight are constructed for the congruence subgroup Γ0(4𝑁) when 𝑠 is even. One can find these forms helpful in revealing the arithmetical meaning of additional terms in the formulas for the number of representations of positive integers by positive quadratic forms with integral coefficients in an even number of variables.

scholarly journals Projective varieties and rings of Thetanullwerte

1990 ◽  
Vol 118 ◽  
pp. 165-176
Author(s):  
Riccardo Salvati Manni
Keyword(s):  
Positive Integer ◽  
Holomorphic Function ◽  
Half Space ◽  
Modular Forms ◽  
Congruence Subgroup ◽  
Integral Closure ◽  
Graded Ring ◽  
Projective Varieties ◽  
Entry Vector

Let r denote an even positive integer, m an element of Q2g such that r·m ≡ 0 mod 1 and ϑm the holomorphic function on the Siegel upper-half space Hg defined by(1) ,in which e(t) stands for exp and m′ and m″ are the first and the second entry vector of m. Let Θg(r) denote the graded ring generated over C by such Thetanullwerte; then it is a well known fact that the integral closure of Θg(r) is the ring of all modular forms relative to Igusa’s congruence subgroup Γg(r2, 2r2) cf. [6]. We shall denote this ring by A(Γg(r2, 2r2)).

scholarly journals Representations by octonary quadratic forms with coefficients 1, 2, 3 or 6

2017 ◽  
Vol 13 (03) ◽  
pp. 735-749 ◽  
Author(s):  
Ayşe Alaca ◽  
M. Nesibe Kesicioğlu
Keyword(s):  
Positive Integer ◽  
Modular Forms ◽  
Quadratic Forms

Using modular forms, we determine formulas for the number of representations of a positive integer by diagonal octonary quadratic forms with coefficients [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text].

scholarly journals Eichler Maps and Hyperbolic Fourier Expansion

1970 ◽  
Vol 40 ◽  
pp. 173-192 ◽  
Author(s):  
Toyokazu Hiramatsu
Keyword(s):  
Positive Integer ◽  
Modular Forms ◽  
Quadratic Forms ◽  
Fourier Expansion ◽  
Automorphic Forms ◽  
Hilbert Modular Forms ◽  
Ternary Quadratic Forms ◽  
Hilbert Modular ◽  
Lecture Notes

In his lecture notes ([1, pp. 33-35], [2, pp. 145-152]), M. Eichler reduced ‘quadratic’ Hilbert modular forms of dimension —k {k is a positive integer) to holomorphic automorphic forms of dimension — 2k for the reproduced groups of indefinite ternary quadratic forms, by means of so-called Eichler maps.

scholarly journals The modular equation and modular forms of weight one

1985 ◽  
Vol 100 ◽  
pp. 145-162 ◽  
Author(s):  
Toyokazu Hiramatsu ◽  
Yoshio Mimura
Keyword(s):  
Modular Forms ◽  
Quadratic Field ◽  
Congruence Subgroup ◽  
Algebraic Integer ◽  
Complex Multiplication ◽  
Cusp Forms ◽  
Imaginary Quadratic Fields ◽  
Modular Equation ◽  
Class Invariants ◽  
Weight One

This is a continuation of the previous paper [8] concerning the relation between the arithmetic of imaginary quadratic fields and cusp forms of weight one on a certain congruence subgroup. Let K be an imaginary quadratic field, say K = with a prime number q ≡ − 1 mod 8, and let h be the class number of K. By the classical theory of complex multiplication, the Hubert class field L of K can be generated by any one of the class invariants over K, which is necessarily an algebraic integer, and a defining equation of which is denoted byΦ(x) = 0.

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